Sorry, checking it again, i saw, that i made a mistake, when i tried to simplify the last chain. The right one is:
If r5c6=6:
r5c4=7, r1c6=7, r3c8=7, r2c2=7,
r3c9=5, (r1c7|r2c7|r3c7=6) r8c7<>6, r8c3=6, r6c2=6

The 3 chains also solve the first puzzle. I noticed, that these "twin sudokus" (2 numbers changed) mostly have very similar solution paths.